Bernard Goetz had the right solution, but he had five shots for four goblins.

No, he didn't. The Goetz case teaches us several salient lessons, but effective self-defense is not one of them.

Honestly, if I were caught in that situation, I don't think I'd be able to do much. As others have mentioned, one shot might spook the gang. It might.

So, what are we left with after that? A mob animal that's spooked and has nowhere to go. All I've done is a) made it more aggressive, and b) focused that on myself.

Frankly, in that situation, I'd simply play the part of the ineffectual urban yuppie and give them my wallet. There's nothing in there that can't be replaced, and I wouldn't be placing lives (both innocent and criminal) in danger.

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Sometimes it’s nice not to destroy the world for a change.
--Randall Munroe